Best Known (178−6, 178, s)-Nets in Base 4
(178−6, 178, large)-Net over F4 — Constructive and digital
Digital (172, 178, large)-net over F4, using
- 5 times m-reduction [i] based on digital (172, 183, large)-net over F4, using
- trace code for nets [i] based on digital (50, 61, 2796233)-net over F64, using
- net defined by OOA [i] based on linear OOA(6461, 2796233, F64, 15, 11) (dual of [(2796233, 15), 41943434, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6461, 5592467, F64, 3, 11) (dual of [(5592467, 3), 16777340, 12]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;192,64) [i]
- linear OOA(6417, 2796201, F64, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6461, 5592467, F64, 3, 11) (dual of [(5592467, 3), 16777340, 12]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6461, 2796233, F64, 15, 11) (dual of [(2796233, 15), 41943434, 12]-NRT-code), using
- trace code for nets [i] based on digital (50, 61, 2796233)-net over F64, using
(178−6, 178, large)-Net in Base 4 — Upper bound on s
There is no (172, 178, large)-net in base 4, because
- 4 times m-reduction [i] would yield (172, 174, large)-net in base 4, but